In contrast to Refs. [1]}, [2]}, here we propose a different type of mapping, in which all sites
of the lattice on which the protein lives host qubits. The approach was inspired by recent D-Wave applications for
homopolymers [3]}, and shares some similarities with a QUBO formulation for lattice
heteropolymers [4]} which, to our knowledge, has not yet been implemented.
The energy \(E\)  is such that its minimization makes the values of the qubits coalesce to a finite set of active qubits
defining the desired folded structure. Importantly from the viewpoint of QA, the entire function
\(E\) , including a self-avoidance term, is manifestly quadratic, or two-local, in the binary spin variables.
This fully distributed dynamical encoding method can be considered as a clustering approach driven by requiring
a legal chain on the lattice. It is also somewhat reminiscent of a molecular field theory [5]} where the fields
reside on a lattice and give rise to structures through their dynamics.
